Problem: What do the following two equations represent? $5x+y = 1$ $-5x+25y = 2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $5x+y = 1$ $y = -5x+1$ Putting the second equation in $y = mx + b$ form gives: $-5x+25y = 2$ $25y = 5x+2$ $y = \dfrac{1}{5}x + \dfrac{2}{25}$ The slopes are negative inverses of each other, so the lines are perpendicular.